Nuclear magnetic resonance (NMR) is a phenomenon whereby the nuclei of certain elements that have a non-zero magnetic moment (for example 1H, 31P, 13C) can interact with a static applied magnetic field to adopt a series of discrete allowed orientations with respect to the direction of the applied field. A radiofrequency magnetic field can then be applied in such a way as to perturb the equilibrium state of the nuclei such that an NMR signal can be detected either in the same coil as used to transmit the radiofrequency magnetic field or in a different radiofrequency receiver coil. The addition of a third type of magnetic field, namely magnetic field gradients, can be used to make the NMR signals spatially dependent. The application of magnetic field gradients in each of the three mutually orthogonal spatial axes (x, y, and z) enables the signals to be encoded in such a way that the detected signals can be processed to produce an image of the object giving rise to the signals. This method is known as magnetic resonance imaging (MRI). The MRI method can be used to produce images of living tissue (usually based on the hydrogen nucleus) in whole animals and humans, and has become a powerful imaging tool both in research and in clinical medicine.
An image generated using MRI is made up of a plurality of small volume imaging elements (also referred to as ‘voxels’), which are defined by an imaging matrix. The imaging matrix may be either a two or three dimensional grid defined relative to the region of an object being sampled. The region of the object being sampled may be referred to as a “field-of-view”, or “sampled region” when image sampling (or imaging) of the region has completed. The size of the voxels determines the spatial resolution of the image, with smaller voxels being able to provide finer image detail (i.e. produce images with higher image resolution) and larger voxels being able to provide less image detail (i.e. produce images with lower image resolution). A standard imaging resolution refers to the spatial resolution of the source image data obtained using a voxel size (defined by an imaging matrix) that is typically used for imaging an object based on a particular imaging technique (such as MRI). For example, in the context of diffusion-weighted MRI, imaging is typically performed based on a voxel size of approximately 2 mm×2 mm×2 mm or larger. The standard imaging resolution applicable as a reference for the system and method described herein may be different in size depending on type or context of the imaging being performed.
The quality of the image will be also influenced by a level of experimental (or background) image noise present. Such noise is commonly measured by a signal-to-noise ratio (SNR). The SNR level in an MRI image is dependent on the size of the voxel. The smaller the voxel size, the smaller the signal, while the noise level is unchanged. Thus, a smaller voxel gives rise to a lower SNR. MRI suffers from an intrinsic limitation in that spatial resolution, SNR, and the time required to acquire images are all strongly interdependent factors. This interdependency makes it difficult to improve any one of these aspects without compromising the others.
A problem with MRI is the trade off between imaging time and the resulting image resolution. MRI imaging on a region using smaller voxels takes significantly more time than MRI imaging on the same region using larger voxels. Various methods have been proposed to produce higher-resolution images of a sampled region using MRI, such as:                Reducing the “field-of-view” of the image, which involves obtaining source image data of a smaller area of an object using the same number of voxels (defined by an imaging matrix within the reduced “field-of-view”) as that typically used for imaging a standard (larger) “field-of-view”, where each voxel has a smaller voxel size;        Increasing the number of acquired voxels, which involves obtaining source image data of a target “field-of-view” using a larger number of acquired voxels (defined by an imaging matrix within the target “field of view”) than that typically used for imaging any “field-of-view”, where each voxel has a smaller voxel size;        Increasing the reconstructed number of voxels by combining source image data acquired from multiple receiver coils (also referred to as “parallel-imaging” MRI); and        Using super-resolution techniques, which involve combining multiple magnetic resonance (MR) images (sampled at a standard imaging resolution) taken with subvoxel-shifts in a slice-direction in order to reconstruct an image with higher-resolution in the slice-direction.        
There are problems with the above approaches. Imaging over a smaller area of an object (with the same imaging matrix size) can provide greater visual detail of that area but at a cost of having less overall visual information. This technique may not be a practical option where the region required for imaging is a larger area than the reduced area being sampled. Where the reduced sample area only covers a subset of the target region required to be sampled, the imaging process needs to be repeat across the entire target region (to maintain the high level of imaging detail), which significantly increases imaging time. MRI images produced based on a small voxel size are more sensitive to errors caused by (e.g. inadvertent) movement of the object during sampling. Such errors are correctable by rescanning the object, but this can take considerable time. “Parallel-imaging” MRI techniques require the use of additional receiver equipment, which increases the technical complexity (and potential for error) in the MRI procedure. The technique of combining information from multiple MR images (taken with subvoxel-shifts in a slice-direction) to produce a higher-resolution image effectively requires additional sampling at subvoxel intervals, which significantly increases the time of performing the MRI procedure.
Super-resolution refers to techniques that in some way enhance the resolution of an imaging system. These techniques typically involve the use of extra information to achieve such a gain in resolution (for example using information from multiple low-resolution images, each with different information content, to generate an image with higher-resolution than any of the source images). However, a problem with super-resolution is the difficulty in identifying the relevant types of information that may be useful for enhancing imaging quality, and also how that information may be efficiently obtained or derived, and used for image enhancement.
Another problem is that MRI images may not effectively illustrate structurally important features (e.g. tissue structure) in the part of the object being sampled. Several techniques have been developed to extract such information. For example, diffusion-weighted imaging (DWI) is a MRI technique that is unique in its ability to probe tissue micro-architecture at the cellular level in vivo in a completely non-invasive manner, by making the MRI images sensitised to the random motion of water molecules. Molecular diffusion refers to the random, microscopic, translational motion of molecules, also known as ‘Brownian motion’. In DWI, magnetic field gradients in a given direction are incorporated, and the resulting DWI images are sensitive to the random, diffusion-induced microscopic displacement of water molecules along the chosen gradient direction. In the case of a free liquid without barriers that hinder diffusion, water molecules will diffuse isotropically (that is, they will diffuse without any preferred direction), and the image intensity of the DWI will be independent on the selected magnetic field gradient direction. On the other hand, in coherently-arranged structures such as in brain white matter, the coherent arrangement of axonal fibres gives rises to the preferential displacement of water molecules along the fibres rather than across them. The image intensity of the DWI image is therefore dependent on the orientation of the fibres at that location relative to the direction along which diffusion sensitisation was applied during the MRI measurement. A number of variants of this DWI method are known, depending on the way the diffusion-sensitisation is applied, the way the images are acquired, the model used to analyse the data, etc.
Information processing in the brain takes place in the grey matter, while white matter connects different grey matter regions, as well as the brain to the rest of the body. At the microscopic level, white matter consists primarily of axonal fibres. These fibres are organized into larger bundles known as ‘tracts’ or ‘fasciculi’, which provide the coherent arrangement of structures that hinders the diffusion of water molecules, and thus influences the image intensity in DWI.
Since the image intensity of the DWI image is dependent on the orientation of the fibres at a given location relative to the direction along which diffusion sensitisation was applied during the MRI measurement, DWI data have been used to infer the main direction of the fibres in the brain. By acquiring multiple DWI images, each sensitised to diffusion along a different direction, enough information can be gathered to infer the orientation of the white matter fibres within each imaging voxel. The diffusion tensor model was the original method used to extract the fibre orientation from DWI data, giving rise to the more general term ‘diffusion tensor imaging’ (DTI), as described in Basser P J, Mattiello J, et al.: “MR diffusion tensor spectroscopy and imaging”, Biophysics Journal 1994; 66, 259-267. With this approach, the signal is modelled assuming a three-dimensional Gaussian diffusion process, and the fibre orientation is assumed to correspond to the direction of fastest diffusion (i.e. the major eigenvector of the diffusion tensor). In this way, a model of the fibre orientation in each voxel can be estimated.
Several properties of the diffusion tensor have been exploited to generate images with various contrasts. Among the most commonly used are the trace of the tensor (a measure of the average diffusivity of the water molecules, averaged uniformly over all directions), and the anisotropy indices (each a measure of the degree of directional-dependence of the diffusion of water molecules).
Image analysis methods that display the directionality of diffusion of water molecules have also been developed, by combining the information of an anisotropy index (typically fractional-anisotropy, or FA) with the directional information contained in the major eigenvector of the diffusion tensor at each voxel location. By assigning a colour (red, green, and blue) for each direction, a directionally-encoded colour (DEC) map is generated, as described in Pajevic S and Pierpaoli C: “Color schemes to represent the orientation of anisotropic tissues from diffusion tensor data: application to white matter fiber tract mapping in the human brain”, Magnetic Resonance in Medicine 1999; 42, 526-540. In these maps, the right-left component of the major eigenvector is set to the red colour, the anterior-posterior component to green, and the superior-inferior component to blue. Given the lack of coherent structures in gray matter, the intensity of the DEC maps are usually weighted by the corresponding intensity of an anisotropy index, to avoid the presence of random colour distributions in gray matter regions. In this way, the DEC maps can be used to visualise white matter architecture over the whole brain. For example, regions of white mater where the fibres run primarily from left to right will appear red, and so on.
Once the orientation of the white matter fibres is known within each imaging voxel, it becomes possible to estimate the path of the white matter connections, by linking this information across several voxels. To date, a number of fibre-tracking algorithms have been proposed to ‘track’ the fibre orientations from one brain region to another. Most fibre-tracking algorithms proposed to date are based on the ‘streamlines’ method, as described in Mori S and van Zijl P C: “Fiber tracking: principles and strategies—a technical review”, NMR in Biomedicine 2002; 15, 468-480. This technique involves ‘tracking’ or following the white matter orientation from a user-specified ‘seed’ point, until the ‘track’ reaches a ‘target’ region, or leaves the white matter, or some other termination criterion is reached. The resultant path through three-dimensional space constitutes what is referred to as a “streamline”. This approach is very sensitive to experimental image noise, as corrupted orientations will cause the track to ‘jump’ into adjacent structures, leading to the inference of connections that do not exist in reality. There is therefore a degree of uncertainty about each generated ‘track’, but the streamlines method provides only a single ‘best guess’ track, with no further information about its uncertainty or other potential paths. To address this issue, a new class of ‘probabilistic’ fibre-tracking algorithms was developed by a number of groups, as described for example by Behrens T E J, et al.: “Non-invasive mapping of connections between human thalamus and cortex using diffusion imaging”, Nature Neuroscience 2003; 6:750-757. These provide a map reflecting the probability of connection to the specified seed point given the level of noise present in the data, thus taking any uncertainty about the orientations into account. It exploits the uncertainty in the data to generate thousands of tracks, the density of which reflects the probability of connection.
Two main ways of performing fibre-tracking can be considered: (i) targeted fibre-tracking, and (ii) whole-brain fibre-tracking. In targeted fibre-tracking, two or more regions-of-interest (ROI) are defined, and tracks that connect between them form a bundle; all other tracks generated are simply discarded. This has obvious limitations. Firstly, it requires significant user interaction (and therefore a potential source of subjectivity and variability). Furthermore, it requires a priori knowledge of the likely connections to select appropriate regions of interest, and typically discards most of the tracks generated. Moreover, connections that were not previously expected will not be identified, which could lead to dangerous misinterpretation of the results. In whole-brain fibre-tracking, on the other hand, tracks are started from many voxels throughout the brain, and no ROIs (seed or target) are required. Therefore, whole-brain fibre-tracking does not rely on the subjective definition of any regions, reducing considerably the user interaction, and making therefore the results less subjective.
Although the diffusion tensor model is still commonly used in the analysis of DWI data, it is now generally accepted that there are serious limitations with this model, in particular in cases where multiple fibre orientations coexist within the same imaging voxel (or ‘crossing fibres’). In these cases, the fibre orientations estimates obtained from the diffusion tensor model are incorrect. As a consequence, using this model will often cause the fibre-tracking algorithm to provide an incorrect delineation of the white matter tracts, thus establishing connections where none exists in reality, or failing to identify existing connections.
To address the crossing-fibres problem, a number of alternatives to the diffusion tensor model have been developed for estimating the orientation of the white matter fibres. One of these alternative models is described in Tournier, J-D., Calamante, F., Connelly, A.: “Robust determination of the fibre orientation distribution in diffusion MRI: non-negativity constrained super-resolved spherical deconvolution”, NeuroImage 2007; 35, 1459-1472. This approach, known as constrained spherical deconvolution (CSD), involves calculating an estimate of the distribution of fibre orientations (the fibre-orientation distribution, or FOD) present within each voxel, and is thus not limited to a single fibre orientation.
It is therefore desired to address one or more of the above issues or problems, or to at least provide a more useful alternative to existing MRI solutions.